V: Bonds
14: Term Structure
of Interest Rates
Term Structure
 $1000
 $1000

(1 Year CDs)
@ 3%

(1.03)(1+X) = ??

(2 Year CD)
@ 4%

(1.04)2
Chapter 14: Term Structure of Interest Rates
= $1081.60
© Oltheten & Waspi 2012
Decreasing Rates
 Let x = 4%
2 (1 Year CDs)
<
$1000(1.03)(1.04) <
<
2 Year CD
$1000(1.04)2
$1081.60
Increase in demand increases
price and decreases yield on
2.year CDs
Chapter 14: Term Structure of Interest Rates
© Oltheten & Waspi 2012
Increasing Rates
 Let x = 6%
2 (1 Year CDs)
>
$1000(1.03)(1.06) >
>
2 Year CD
$1000(1.04)2
$1081.60
Decrease in demand decreases
price and increases yield on
2.year CDs
Chapter 14: Term Structure of Interest Rates
© Oltheten & Waspi 2012
Equilibrium
 The market predicts
2 (1 Year CDs)
=
$1000 (1.03)(1+X) =
X
=
2 Year CD
$1000 (1.04)2
5.0097%
Half the smart money is on
lower rates and half the
smart money is on higher
rates
Chapter 14: Term Structure of Interest Rates
© Oltheten & Waspi 2012
Term Structure
Theoretical Predictions
7%
6.0%
6%
Yield Curve
5.0%
5%
4.5%
4.0%
4.7%
4%
4.0%
3.0%
3%
3.0%
4.0%
2%
2.0%
1%
0%
1
1.5
2
Chapter 14: Term Structure of Interest Rates
2.5
3
3.5
4
4.5
5
© Oltheten & Waspi 2012
Yield Curve 1999-2013
Chapter 14: Term Structure of Interest Rates
© Oltheten & Waspi 2012
Normal Yield Curves
Chapter 14: Term Structure of Interest Rates
© Oltheten & Waspi 2012
Flat Yield Curves
8%
7%
1999
6%
2006
5%
2005
4%
3%
2%
1%
0%
0
5
10
Chapter 14: Term Structure of Interest Rates
15
20
25
30
© Oltheten & Waspi 2012
35
Inverted Yield Curve
7%
6%
2000
2006
2007
5%
4%
3%
2%
1%
0%
0
5
10
Chapter 14: Term Structure of Interest Rates
15
20
25
30
© Oltheten & Waspi 2012
35
Yield Curve 2007-2013
Chapter 14: Term Structure of Interest Rates
© Oltheten & Waspi 2012
Deriving the Yield Curve
 Yield is a function of






Term to maturity
Coupon rate
Call provisions
Liquidity
Risk of Default
Tax implications
Chapter 14: Term Structure of Interest Rates
© Oltheten & Waspi 2012
Treasury Securities
 Represents debt of the US Department of
the Treasury
 Largest most liquid capital market in the
world
 Trade in terms from 1 day to 30 years
Chapter 14: Term Structure of Interest Rates
© Oltheten & Waspi 2012
Deriving Term Structure
 Yield is a function of






Term to maturity
Coupon rate
Call provisions
Liquidity
Risk of Default
Tax implications
Chapter 14: Term Structure of Interest Rates
Don’t have to worry about
these any more
© Oltheten & Waspi 2012
Treasury Securities
 T-Bills
 < 1 year
 Discount paper
 T-Notes
 2years to 10 years
 Semi-annual coupon
 T-Bonds
 >10 years
 Semi-annual coupon
Chapter 14: Term Structure of Interest Rates
© Oltheten & Waspi 2012
Observation #1: 6 month rate
 Bloomberg shows
 6 month T-Bill trading at a yield of 8%*
*hypothetical data
Chapter 14: Term Structure of Interest Rates
© Oltheten & Waspi 2012
Yield Curve
9.0%
8.5%
8.0%
7.5%
7.0%
0
6
Chapter 14: Term Structure of Interest Rates
12
18
24
© Oltheten & Waspi 2012
Observation 2: 12 month rate
 Bloomberg shows
 12 month T-Bill trading at a yield of 8.3%*
*hypothetical data
Chapter 14: Term Structure of Interest Rates
© Oltheten & Waspi 2012
Yield Curve
9.0%
8.5%
8.0%
7.5%
7.0%
0
6
Chapter 14: Term Structure of Interest Rates
12
18
24
© Oltheten & Waspi 2012
Observation #3: 18 month rate
 Bloomberg shows

18 month 8.5% T-Note trading at a yield of 8.9%*
18 month
12 month
8.5%
0%
Yield: 8.3%
Yield: 8.9%
 Is the 0.6% increase in yield because the bond is 6
months longer or because it has coupon
payments?
Chapter 14: Term Structure of Interest Rates
© Oltheten & Waspi 2012
Yield Curve
8.9%
9.0%
?%
8.5%
8.3%
8.0%
8.0%
7.5%
8.5%
7.0%
0
6
Chapter 14: Term Structure of Interest Rates
12
18
24
© Oltheten & Waspi 2012
Buy the Note …
Department of the Treasury
Principal Sum of $10,000 due April 15, 2015
with interest calculated at 8.5%
$425
$425
$425
April 15, 2014
October 15,
2014
April 15, 2015
Chapter 14: Term Structure of Interest Rates
© Oltheten & Waspi 2012
1. ... for a total of $9,944.97
$10,425
 .089
1 

2 

$425
 .089
1 

2 

$406.89
Chapter 14: Term Structure of Interest Rates
3
 $9,148.52
$425
 .089
1 

2 

$389.56
2
© Oltheten & Waspi 2012
2. Remove the coupons
Department of the Treasury
Principal Sum of $10,000 due April 15, 2015
with interest calculated at 8.5%
$425
April 15, 2014
$425
$425
April 15, 2015
October 15,
2014
Chapter 14: Term Structure of Interest Rates
© Oltheten & Waspi 2012
3. Sell the coupons separately
$425
April 15, 2014
$425
October 15,
2014
Chapter 14: Term Structure of Interest Rates
$425
 $408.65
 .080
1 

2 

$425
 .083
1 

2 

2
 $391.81
© Oltheten & Waspi 2012
4. Sell the final coupon and principal …
Department of the Treasury
Principal Sum of $10,000 April 15, 2015
with interest calculated at 8.5%
$425
April 15,
2015
Chapter 14: Term Structure of Interest Rates
© Oltheten & Waspi 2012
… for $9,144.51
Price of the 18 month note
Proceeds from 6 month coupon
Proceeds from 12 month coupon
Required proceeds
from the 18 month coupon and principal
Chapter 14: Term Structure of Interest Rates
© Oltheten & Waspi 2012
5. Which determines the zero coupon yield
$10,425
April 15, 2015
$10,425
 Yd 
1 

2 

3
 $9,144.51
 $10,425  
  1
Yd  2 3

 $9,144.51 
Yd  0.0893
Chapter 14: Term Structure of Interest Rates
© Oltheten & Waspi 2012
Yield Curve
8.9%
9.0%
8.93%
8.5%
8.3%
8.0%
8.0%
7.5%
7.0%
0
6
Chapter 14: Term Structure of Interest Rates
12
18
24
© Oltheten & Waspi 2012
Yield Curve
9.0%
8.93%
8.5%
8.3%
8.0%
8.0%
7.5%
7.0%
0
6
Chapter 14: Term Structure of Interest Rates
12
18
24
© Oltheten & Waspi 2012
Observation #4: 24 month rate
 Bloomberg shows

24 month 9% T-Note trading at a yield of
8.92%
 Calculate the 24 month zero-coupon yield
*hypothetical data
Chapter 14: Term Structure of Interest Rates
© Oltheten & Waspi 2012
Yield Curve
9.5%
8.93%
9.0%
8.5%
8.3%
8.0%
8.0%
7.5%
7.0%
0
6
Chapter 14: Term Structure of Interest Rates
12
18
24
30
© Oltheten & Waspi 2012
Bonds III